Two beers

Right!
I don't actually have an answer here, so don't get your hopes up, but your thoughts please!

I buy two bottles of cold beer at the bar, they're both taken out of the fridge and opened at the same time. I'm holding one in each hand. I can only down a few before my stomach gets full and the following dilemma sets in:

Asssuming I drink steadily, and assuming I prefer cold beer to warm beer, is it better to drink all of one bottle before starting the other, or to take alternate sips from each?

Ponder...! (and if you feel like it, think of fizziness too, to make it interesting).

I would probably say that you would be better off drinking all of one bottle then the other. This is because there is more liquid in the untouched bottle so will remain cooler for longer as it will take more time for your hand to warm it up. If you drank the two alternating, then as the amount of liquid decreases, they will both get warmer more quickly.

This is talking from a little experience.... maybe I should test this theory.

There are so many variables here...I'm going to assume you hold the bottle by the neck and introduce very little heat into it, so that the rate of heating unheld is nearly the same as the rate of heating when held. So the beer is mostly being warmed by the ambient air. I'm also going to neglect second order effects like surface area and outgassing rates.

The temperature differential is small enough that we can use Newton's cooling law :

Now, if beer is being drunk out of only one bottle for a given period, for that bottle we have

m(t) = m0[1 - t/B] and for the other bottle (which is waiting, untouched) we have

m(t) = m0, during this same period. After the first bottle is drunk, the second bottle's mass behaves like the first for the subsequent period.

If beer is being drunk from both bottles, their mass behaviors are identical, and are given by

m(t) = m0[1 - t/2B]

In the above expressions,
m0 = initial mass of beer, and
B = time taken to drink one bottle of beer.

Now we have the necessary framework. We simply plug in for m(t) in the different scenarios and get separable differential equations. These can be solved to find T(t) for each of the bottles in each of the cases (quite easily).

(For instance, when drinking one-at-a-time, for the beer that is drunk first :

T(t) = T0 - (T0 - Ti)*exp[-K*m0*t(1 - t/2B)]

I've run out of patience, and decided not to calculate the others, but they can be done just as easily.)

Now, the last step is to relate the extent of dislike to the temperatures. Let's say the extent of dislike is a linear function of the temperature. Then the objective is to determine which of the 2 cases gives the lower time integrated temperature (integrated over the times that each beer is being consumed).

Do all of these things and plug in realistic numbers to get a complete (well ???) solution.

5> Decision time (now which did I like better...mmm...the chicks were better on the second round...don't remember the first time too well...burp...I need another beer or two) go to step 1 (and increment number of p's before each 'pop' by 5)

6> Bartender drags your senseless body out and dumps it on the sidewalk where you enjoy a blissful slumber.

Well I'm 20 now (drinking age 18), but was 15 when we started going to this place, where it's so busy that it makes sense to buy in bulk at the bar. It's only 60p a bottle, so the algorithm suggested by TenaliRaman is almost always used, and after around step 4 nobody cares how cold they are anyway.

Thanks to Gokul for that valiant effort in gathering the preliminary data for this experiment. Clearly, we now see there is an order effect, so we need to design the experiment to cancel that out. A cross-over design seems the only way to handle this. Here's the experimental plan. Gather several drinking buddies, erm, subjects. Buy each of them 2 beers. Half of them should drink alternately from both bottles, and the other half should drink the bottles sequentially. Have them rate the two bottles of beer. Now, buy them 2 more beers. The half that drank alternately now should drink sequentially, and vice versa. Have them rate the two bottles again.

Oh, drat, there still may be an inter-observer variation...this is the difficulty when relying on subjective measures. Better incorporate a repeated measures component just to be certain. Day 2, take the same group of drinking budd...sorry...subjects...and again buy them two beers. The group that started out with alternating bottles on Day 1 should start out sequentially this time, and those that started out sequentially last time should drink alternatingly this time. Otherwise, conduct the experiment for Day 2 the same as for Day 1.

There are so many variables here...I'm going to assume you hold the bottle by the neck and introduce very little heat into it, so that the rate of heating unheld is nearly the same as the rate of heating when held. So the beer is mostly being warmed by the ambient air. I'm also going to neglect second order effects like surface area and outgassing rates.

The temperature differential is small enough that we can use Newton's cooling law :

Now, if beer is being drunk out of only one bottle for a given period, for that bottle we have

m(t) = m0[1 - t/B] and for the other bottle (which is waiting, untouched) we have

m(t) = m0, during this same period. After the first bottle is drunk, the second bottle's mass behaves like the first for the subsequent period.

If beer is being drunk from both bottles, their mass behaviors are identical, and are given by

m(t) = m0[1 - t/2B]

In the above expressions,
m0 = initial mass of beer, and
B = time taken to drink one bottle of beer.

Now we have the necessary framework. We simply plug in for m(t) in the different scenarios and get separable differential equations. These can be solved to find T(t) for each of the bottles in each of the cases (quite easily).

(For instance, when drinking one-at-a-time, for the beer that is drunk first :

T(t) = T0 - (T0 - Ti)*exp[-K*m0*t(1 - t/2B)]

I've run out of patience, and decided not to calculate the others, but they can be done just as easily.)

Now, the last step is to relate the extent of dislike to the temperatures. Let's say the extent of dislike is a linear function of the temperature. Then the objective is to determine which of the 2 cases gives the lower time integrated temperature (integrated over the times that each beer is being consumed).

Do all of these things and plug in realistic numbers to get a complete (well ???) solution.

You also have to take into effect the consistency of the beer itself, A light beer i.e. Miller Light versus a thicker beer such as Guiness. The beers would have slightly different cooling effects because of the way they retain temperature. Also, you have take into effect the material the bottle is made out of and wether or not it was sitting on the counter when he wasn't drinking it. If the counter was metal and the ambient air was cool, it would cool differently than if the counter was wood. Also, are you a cold hearted bastard? Then your hands would be ice cold.

You also have to take into effect the consistency of the beer itself, A light beer i.e. Miller Light versus a thicker beer such as Guiness. The beers would have slightly different cooling effects because of the way they retain temperature. Also, you have take into effect the material the bottle is made out of and wether or not it was sitting on the counter when he wasn't drinking it. If the counter was metal and the ambient air was cool, it would cool differently than if the counter was wood. Also, are you a cold hearted bastard? Then your hands would be ice cold.

:surprised Guiness isn't supposed to be served ice cold!!! No, no, no, it's a sacrilege! And does it really matter if Miller Light is warm or cold, it seems it would be bad either way :yuck: Guess it just depends if you're one of those people who likes your water chilled or served room temperature.

You know, this must be a male thing -- this isn't the first time I have heard a guy mention dilema involving "beer drinking". Try opening one, if you open them both the carbination will leave the bottle and make it flat and or hot... then drink the other.. Oh and don't hold onto both of them, put one down, your body heat will warm the liquid.